A conventional circuit for reproducing an analog waveform by converting a digital signal into an analog signal, including a D/A (Digital to Analog) converter for decoding and step-pulsing, and a post-filter (identical to a low pass filter), has been well known. This circuit involved a quantization error from a desired target waveform in a range from −½ LSB to +½ LSB (e.g., refer to Iwao Sagara, “Introduction to AD/DA Conversion Circuit, P.68 to P.75, P.80 and P.81).
FIG. 11 is a block diagram showing one example of the conventional waveform generation circuit. In FIG. 11, 1 denotes an address generator for generating the address value of a memory, and 2 denotes a waveform memory for storing waveform data. 3 denotes a D/A (Digital to Analog) converter for converting a digital value into an analog value in accordance with an output value of the waveform memory 2, and 4 denotes a low pass filter for removing high frequency components of output of the D/A converter 3 to make the waveform smoother. 5 denotes a timing controller for supplying necessary control signals such as a clock signal and an enable signal to the address generator 1 and the D/A converter 3. This waveform generation circuit may be employed as a speech synthesis unit by adding an amplifier for amplifying power and a speaker.
In FIG. 11, the waveform memory 2 preliminarily stores waveform data desired to generate waveform, the waveform data being arranged in time series. The timing controller 5 generates a control signal such as a trigger signal to output a memory address value to the address generator 1 at regular time intervals. The timing controller 5 generates a control signal such as a chip select signal required for memory output to the waveform memory 2, and outputs a trigger signal or a select signal required for D/A conversion to the D/A converter 3.
The address generator 1 outputs the address value in the order from the initial address of waveform data stored in the waveform memory 2 in synchronism with a trigger signal received from the timing controller 5 at regular time intervals. The waveform memory 2 outputs waveform data according to the address value output from the address generator 1. The D/A converter 3 outputs a voltage proportional to a value output from the waveform memory 2, if the value is set. The low pass filter (LPF) 4 removes a sampling noise produced in accordance with an output period of the D/A converter 3.
FIG. 12 shows the basic concept of a waveform generation method for use with the conventional waveform generation circuit. In FIG. 12, 101 is a target waveform to be generated, and 104 denotes a D/A output waveform. The conventional waveform generation circuit determined the output by performing a so-called quantization involving selecting a value of the D/A converter closest to a waveform value of analog quantity at a regular interval sampling time Ts, if the target waveform 101 was given. The D/A output waveform 104 represents the output voltage values in time series, which are supplied from the D/A converter 3 at regular intervals.
FIG. 13 is an enlarged view of FIG. 12. In FIG. 13, an output point 102 of the D/A converter 3 is selected at a value close to the target waveform, but a quantization error as large as ½ LSB at maximum occurs at the regular interval sampling time Ts, as compared with a transit point 103 of the target waveform at the same point of time. That is, the quantization error δ falls in a range from −½ LSB to +½ LSB.
FIG. 14 is a block diagram showing one example of the configuration of an FM-CW radar apparatus. Herein, 801 denotes a modulation circuit, 802 denotes an oscillator, 803 denotes a directional coupler, 804 denotes a transmission antenna, 805 denotes a reception antenna, 806 denotes a mixer, 807 denotes an amplifier, 808 denotes an A/D (Analog to Digital) converter, 809 denotes frequency analysis means, 810 denotes target detecting means, and 811 denotes distance/speed calculating means (e.g., refer to S. A. Hovanessian, “Radar System Design & Analysis”, Artech House, INC., p.78 to p.81).
In FIG. 14, first of all, the modulation circuit 801 generates a frequency modulation (hereinafter referred to as FM (Frequency Modulation)) signal, which is sent to the oscillator 802. The oscillator 802 generates a high frequency signal modulated with the FM signal and the high frequency signal being distributed by the directional coupler 803 is sent to the transmission antenna 804 and the mixer 806. The transmission antenna 804 radiates a transmitting wave of the high frequency signal toward a target object in front of the radar apparatus. Herein, when the target object exists, a receiving wave (reflected wave) with a time lag is received by the reception antenna 805, and sent to the mixer 806. The mixer 806 generates a signal of frequency difference (hereinafter referred to as a beat signal) between this reflected wave and the transmitting wave distributed by the directional coupler 803. This beat signal is sent to the amplifier 807. The amplifier 807 amplifies the beat signal, and then sent to the A/D converter 808.
The A/D converter 808 converts the beat signal from analog to digital signal form, the beat signal in digital form is then sent to the frequency analysis means 809. The frequency analysis means 809 inputs the digitized beat signals and provides a frequency distribution (frequency spectrum) through the processing of FFT (Fast Frequency Transform) etc. The target detecting means 810 compares the frequency distribution with a threshold, and detects the target value as the largest one of the values beyond the threshold. The distance/speed calculating means 811 calculates the relative distance and relative speed of the target object based on a frequency picked up by the target detecting means 810.
FIG. 15 and FIGS. 16(a) and 16(b) are views for explaining how to calculate the relative distance and relative speed of the target object. FIG. 15 shows variations in the frequency, and FIGS. 16(a) and 16(b) show a frequency spectrum of the beat signal simply. In FIG. 15, 812 denotes a transmitting frequency of the FM-CW radar apparatus, and 813 denotes a receiving frequency.
First of all, the transmitting frequency 812 is linearly increased in an UP slope interval Tmu, and linearly decreased in a DOWN slope interval Tmd to transmit electric wave. Herein, it is supposed that a measuring object exists at the relative speed v and the relative distance R to the FM-CW radar apparatus. At this time, if the transmitting frequency is changed by Δf at the light speed C [m/s] and the transmitting wavelength λ[m] in the time intervals Tmu and Tmd, the Doppler frequency fd is represented by a function (1). Herein, the distance frequency fr caused by a time difference between the transmitting frequency and the receiving frequency, which is proportional to the distance, is represented by a function (2). Also, the beat frequency fb1 in the Up slope interval Tmu and the beat frequency fb2 in the DOWN slope interval Tmd are represented by functions (3) and (4), respectively.fd=2·V/λ  (1)fr=(2R·Δf)/(C·Tm)  (2)fb1=|fd−fr|  (3)fb2=|fd+fr|  (4)
Also, when the distance frequency fr is greater than the Doppler frequency fd, a function (5) holds.2fr=fb1+fb2  (5)
By the way, substituting the function (2) for the function (5), a function (6) for calculating the relative distance from the FM-CW radar apparatus to the target object is derived.R=(C·Tm)·(fb1+fb2)/(4·Δf)  (6)
From the function (6), the distance to the target object is calculated from the beat frequency fb1 in the UP slope interval Tmu and the beat frequency fb2 in the DOWN slope interval Tmd. Also, if the distance frequency fr is calculated, the relative speed V is obtained from the functions (1), (3) and (4).
The conventional radar apparatus for measuring the distance with the FM modulation supplies a voltage of staircase shape to a voltage controlled oscillator to improve the distance measurement precision. At this time, the frequency measuring means measures an output frequency from the voltage controlled oscillator. The frequency measuring means measures the output frequency from the voltage controlled oscillator, corresponding to each voltage of staircase shape, and calculates an applied voltage for making the sweep speed invariable from this measured frequency. Control means operated the distance measurement by supplying this applied voltage to the voltage controlled oscillator at a predetermined interval. (e.g., refer to JP-A-2002-156447).
The conventional waveform generation circuit produced a quantization error of ½ LSB at maximum from the target waveform if the output control for the D/A converter is made at an equal time interval. Also, when a micro signal is dealt with, a periodical ripple noise occurred due to the quantization error of the D/A converter.
FIGS. 17(a) and 17(b) show how the ripple noise occurs due to the quantization error. FIG. 17(a) shows the relationship between the target waveform and the D/A output waveform, and FIG. 17(b) shows the relationship between the D/A output waveform and the output waveform of the low pass filter. For the simplified explanation, the target waveform is linear. 901 denotes a target waveform, 902 denotes a D/A output waveform output from the D/A converter 3 by quantizing the target waveform 901, and 903 denotes the output of the low pass filter 4 disposed at the latter stage of the D/A converter 3 and provided to remove the sampling noise.
As seen from FIG. 17(a), when the minimum step width of the quantization output is rough relative to the target waveform 901, the error between the output voltage of the D/A converter 3 and the target waveform is periodically greater. As a result, the output waveform is undulated as indicated by the output 903 of the low pass filter 4 in FIG. 17(b), so that a ripple noise of the low frequency that is the sampling frequency divided by an integer (¼, ⅕, etc.) appears superposed on the ideal target waveform.
Conventionally, it was required to increase the number of bits or the sampling frequency in the D/A converter to reduce this ripple noise, so that the cost was increased.
Also, the FM-CW radar apparatus for measuring the distance by applying the frequency modulation was required to make the high precision modulation control, but if the modulation signal has the superposed ripple noise, the beat signal as a difference between the transmitting wave and the receiving wave was distorted, causing the frequency spectrum to split or the other peak to arise at a position off the center of the frequency spectrum.
FIGS. 18(a), 18(b) and 18(c) are graphs showing the frequency spectrum of the beat signal for the FM-CW radar apparatus. 904 denotes a frequency spectrum of the beat signal in the UP slope or the DOWN slope. When the transmitting frequency is linearly changed, the beat signal is stable and has one frequency, and the peak value appears sharply as indicated by the frequency spectrum 904 in FIG. 18(a), and then the peripheral portion is at the side lobe level following a window function.
However, if the transmitting frequency is not correctly linear but has the superposed ripple noise, another peak appears at a position off the peak frequency by an amount of frequency according to the period of ripple noise.
FIG. 18(b) shows an instance where the frequency of ripple noise is near the resolution of spectrum, and the maximal point arises halfway on the spectrum of the beat signal. FIG. 18(c) shows an instance where the ripple frequency is higher and sufficiently away from the spectrum of the beat signal. In FIGS. 18(b) and 18(c), there is an obstacle to calculate the distance to the target object.
Conventionally, the D/A converter for use in the modulation circuit for the FM-CW radar apparatus was required to increase the number of bits or the sampling number to make the high precision control. Therefore, the cost was increased.